摘   要：非线性卡尔曼滤波在我们的生产生活中随处可见，在航空航天中的目标定位与跟踪，卫星导航等方面广泛应用。因此非线性卡尔曼滤波的研究具有重要的意义。扩展卡尔曼滤波和无味卡尔曼滤波是非线性卡尔曼滤波的主要代表。扩展卡尔曼滤波是基于泰勒级数展开，将非线性系统函数线性化，再按照卡尔曼滤波原理，对非线性系统进行滤波；无味卡尔曼滤波是基于无味变换的一种非线性滤波算法。

本文首先仿真实现了扩展卡尔曼滤波和无味卡尔曼滤波，并在随机、曲线、直线等三种轨迹环境下，验证了两证算法的性能。仿真结果表明，扩展卡尔曼滤波和无味卡尔曼滤波都有较好的滤波效果，但在滤波结果的精度上，无味卡尔曼滤波是要高于扩展卡尔曼滤波的。

在此基础上，本文设计了一个基于MATLAB GUI的非线性卡尔曼滤波仿真软件，该软件包含一个主界面、三个子界面，三个子界面分别是扩展卡尔曼滤波界面、无味卡尔曼滤波界面和误差对比界面。运行结果表明，本文设计的仿真软件具有良好的交互性能，能够实现扩展卡尔曼和无味卡尔曼的滤波仿真。

关键词：MATLAB；扩展卡尔曼滤波；无味卡尔曼滤波 

  Abstract：Nonlinear Kalman filtering can be seen everywhere in our production and life, and it is widely used in target positioning and tracking, satellite navigation, and so on. Therefore, it is of great significance to explore nonlinear Kalman. Extended Kalman filtering and Unscented Kalman filter are the key representatives of the nonlinear Kalman. Extended Kalman filter is based on the Taylor series expansion, which can make nonlinear function systems linear, and then the system will filter for nonlinear systems. Unscented Kalman filter is a nonlinear filtering algorithm based on unscented transform.

In this paper, we first simulate the Extended Kalman filter and the Unscented Kalman filter, and confirm the performance of both algorithm through three methods, such as random, curve and straight line. The results show that the Extended Kalman filter and the Unscented Kalman filter both have nice filtering effects, and the odorless Kalman filter has a better performance than the extended Kalman filter.

Based on the simulation, the paper presents a nonlinear simulation software of Kalman filtering based on MATLAB GUI, the software contains a main interface and three sub interface, the three sub interface interface include the extended Kalman, Unscented Kalman filter interface and error comparing interfaces. Results show that the software has a good performance, and can realize the simulation of the Kalman filtering and Unscented Kalman filtering.

Keywords: MATLAB; Extended Kalman filtering and Unscented Kalman filter

目  录

第一章 绪论 1

1.1 非线性卡尔曼滤波研究背景介绍 1

1.2 非线性滤波算法的研究现状和趋势 2

1.3 选题的目的和意义 4

1.4 论文内容安排 4

第二章 MATLAB及GUI简介 5

2.1 MATLAB简介 5

2.2 MATLAB GUI简介 7

2.3 本章小结 11

第三章 EKF和UKF算法 12

3.1扩展卡尔曼滤波算法 12

3.1.1卡尔曼滤波算法 12

3.1.2 扩展卡尔曼滤波算法